Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _________ to __________ times of its initial length if the water is to be boiled in 15 minutes.

A diatomic gas $$(\gamma=1.4)$$ does $$100 \mathrm{~J}$$ of work in an isobaric expansion. The heat given to the gas is :

If $$M_0$$ is the mass of isotope $${ }_5^{12} B, M_p$$ and $$M_n$$ are the masses of proton and neutron, then nuclear binding energy of isotope is:

A given object takes $$\mathrm{n}$$ times the time to slide down $$45^{\circ}$$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $$45^{\circ}$$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :